trureturingGitHub MATHEMATICAL ATLAS

Zeros / CONCEPT

Edge Transposition Generation

The swaps across the edges of a finite connected graph generate every permutation of its vertices.

Closed Authored exposition
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES1
PROOF DEPTH0
DOCUMENT LINKS1
THEOREM

Connected edge transpositions generate the full symmetric group

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Edge Transposition GenerationEdge Transposition GenerationThe spectral gap of a connected Hamming-weight gate patternThe spectral gap of a connectedHamming-weight gate pattern
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Certified topology / UPSTREAM

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None recorded in this release.

Certified topology / DOWNSTREAM

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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Zeros
Node ID
D5/S3/Zeros/EdgeTranspositionGeneration
Repository path
D5/S3/Zeros/EdgeTranspositionGeneration.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

Authority boundary

Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.